Continuum model of cell motility and chemotaxis

The paper is devoted to the modelling of chemotaxis within continuum physics. The cells are regarded as active (or self-propelled) oriented particles. Cells, extracellular liquid and chemical attractant are modelled as a fluid mixture. The balance of mass and linear momentum follows the standard scheme of fluid mixtures. The balance of angular momentum, instead, is established by ascribing the cells also an orientational momentum and hence the cell constituent is viewed as a micropolar fluid of rigid particles. A more explicit account of the dynamics of the cell constituent is obtained by restricting attention to a plane orientational motion. The orientational motion is determined by a body couple density, which tends to align the director in the direction of the gradient of the attractant density, and an interaction torque between the cells and the extracellular liquid. The balance equations, for the mass density and the velocity of the cells, are shown to provide a hyperbolic equation for the excess mass density. A detailed comparison with other approaches and results is also given.